Q. 24.6( 12 Votes )

# If a and b are distinct real numbers, show that the quadratic equation 2 (a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots.

Answer :

Given: 2 (a2 + b2)x2 + 2(a + b)x + 1 = 0

Comparing with standard quadratic equation ax2 + bx + c = 0

a = 2 (a2 + b2), b = 2(a + b), c = 1

Discriminant D = b2 – 4ac

= [2(a + b)]2 – 4. 2 (a2 + b2).1

= 4(a2 + b2 + 2ab) – 8 a2 – 8b2

= 4a2 + 4b2 + 8ab – 8a2 – 8b2

= – 4a2 – 4b2 + 8ab

= – 4(a2 + b2 – 2ab)

= – 4(a – b)2 < 0

Hence the equation has no real roots.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Get To Know About Quadratic Formula42 mins
Quiz | Knowing the Nature of Roots44 mins
Take a Dip Into Quadratic graphs32 mins
Foundation | Practice Important Questions for Foundation54 mins
Nature of Roots of Quadratic EquationsFREE Class
Getting Familiar with Nature of Roots of Quadratic Equations51 mins
Champ Quiz | Quadratic Equation33 mins
Quadratic Equation: Previous Year NTSE Questions32 mins
Balance the Chemical Equations49 mins
Champ Quiz | Quadratic Equation48 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses